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Results (16 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
4732.2-a1 4732.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.175111233$ 0.264743301 \( -\frac{10824513276632329}{21926008832} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -4609\) , \( 120244\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-4609{x}+120244$
4732.2-b1 4732.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.193322852$ 0.902067286 \( \frac{14283778547303}{186368} a - \frac{4170573974757}{93184} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 124 a - 171\) , \( -803 a + 394\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(124a-171\right){x}-803a+394$
4732.2-b2 4732.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.193322852$ 0.902067286 \( \frac{27512189178035}{4961861632} a + \frac{12113688444791}{2480930816} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 24 a + 27\) , \( -34 a + 147\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(24a+27\right){x}-34a+147$
4732.2-c1 4732.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.193322852$ 0.902067286 \( -\frac{14283778547303}{186368} a + \frac{5942630597789}{186368} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -125 a - 46\) , \( 802 a - 408\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-125a-46\right){x}+802a-408$
4732.2-c2 4732.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.193322852$ 0.902067286 \( -\frac{27512189178035}{4961861632} a + \frac{51739566067617}{4961861632} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -24 a + 51\) , \( 34 a + 113\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-24a+51\right){x}+34a+113$
4732.2-d1 4732.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.211690204$ $0.533192753$ 1.706459444 \( -\frac{1207949625}{332678528} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -22\) , \( 884\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-22{x}+884$
4732.2-e1 4732.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.220089901$ 4.159308180 \( -\frac{117707714055526111767}{700388906893312} a - \frac{5825725329423279627}{350194453446656} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1938 a + 467\) , \( 34770 a - 41587\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-1938a+467\right){x}+34770a-41587$
4732.2-e2 4732.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.220089901$ 4.159308180 \( \frac{117707714055526111767}{700388906893312} a - \frac{129359164714372671021}{700388906893312} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 1938 a - 1471\) , \( -34770 a - 6817\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(1938a-1471\right){x}-34770a-6817$
4732.2-e3 4732.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.220089901$ 4.159308180 \( \frac{71903073502287}{60782804992} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 866\) , \( 6445\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+866{x}+6445$
4732.2-e4 4732.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.110044950$ 4.159308180 \( \frac{8511781274893233}{3440817243136} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -4254\) , \( 59693\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-4254{x}+59693$
4732.2-e5 4732.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.055022475$ 4.159308180 \( \frac{3389174547561866673}{74853681183008} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -31294\) , \( -2081875\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31294{x}-2081875$
4732.2-e6 4732.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.055022475$ 4.159308180 \( \frac{22868021811807457713}{8953460393696} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -59134\) , \( 5547693\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-59134{x}+5547693$
4732.2-f1 4732.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.051746300$ 4.613806728 \( \frac{4019679}{8918} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 3\) , \( -5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+3{x}-5$
4732.2-g1 4732.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.868936999$ $0.256426207$ 6.063650696 \( -\frac{424962187484640625}{182} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -15663\) , \( -755809\bigr] \) ${y}^2+{x}{y}={x}^{3}-15663{x}-755809$
4732.2-g2 4732.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.289645666$ $0.769278622$ 6.063650696 \( -\frac{795309684625}{6028568} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -193\) , \( -1055\bigr] \) ${y}^2+{x}{y}={x}^{3}-193{x}-1055$
4732.2-g3 4732.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 7 \cdot 13^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.096548555$ $2.307835866$ 6.063650696 \( \frac{37595375}{46592} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 7\) , \( -7\bigr] \) ${y}^2+{x}{y}={x}^{3}+7{x}-7$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.